A the core of any autonomous rendezvous guidance system must be two algorithms for solving Lambert's and Kepler's problems, the two fundamental problems in classical astrodynamics. Lambert's problem is to determine the trajectory connecting specified initial and terminal position vectors in a specified transfer time. The solution is the initial and terminal velocity vectors. Kepler's problem is to determine the trajectory that stems from a given initial state (position and velocity). The solution is the state of an earlier or later specified time. To be suitable for flight software, astrodynamics algorithms must be totally reliable, compact, and fast. Although solving Lambert's and Kepler's problems has challenged some of the world's finest minds for over two centuries, only in the last year have algorithms appeared that satisfy all three requirements just stated. This paper presents an evaluation of the most highly regarded Lambert and Kepler algorithms.